smitakokne wrote:
Is m+z > 0
(1) m-3z > 0
(2) 4z-m > 0
Responding to a pm:
Quote:
When I look at such question, I know I will figure out something if I consider both statements together. I feel comfortable with applying inequalities rules there.
But I find it harder to approach individual statements in such cases. I get lost in figuring out cases to reject (or approve) one statement on its own. At times, I take time and eventually rush onto considering both statements together.
Can you please help me out if I'm lacking some approach or concepts?
There really isn't one suitable method for all inequality questions. The approach depends on the kind of question. Very rarely will I plug in numbers here to find cases where the inequality holds or does not hold.
This is how I will do this question:
"Is m+z > 0?"
Here I think that m and z could both be positive or one of them could be positive with greater absolute value than the other. If both are negative, this doesn't hold. Go on to stmnts.
(1) m-3z > 0
Here, I will try to segregate the variables to get relation between them.
m > 3z
The moment I see this, I naturally go to the number line.
(z positive):
______________________________ 0 ____z_________________3z___________m____________________
OR
(z negative):
__3z_________(m)______________z___(m)__ 0 _______________(m)____________________
Both z and m could be positive, both negative or z negative m positive. Not sufficient.
(2) 4z-m > 0
4z > m
(z positive):
__________________(m)____________ 0 __(m)_______z_____________________(m)_____4z______
OR
(z negative):
______m_______4z____________________z_____ 0 _______________________
Both z and m could be positive, both negative or m negative z positive. Not sufficient.
Both together,
3z < m < 4z
(z positive):
______________________________ 0 ____z_________________3z_____m_______4z___________
OR
(z negative):
___________4z________3z___________________z_____ 0 _______________________
m has to be to the left of 4z but right of 3z. Not possible.
So m and z both must be positive. So m + z > 0
Answer (C)
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Karishma
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